Some fixed point theorems on non-convex sets
DOI:
https://doi.org/10.4995/agt.2017.7452Keywords:
fixed points, nonexpansive mappings, T-regular set, k-uniform convex Banach spaces, Opial propertyAbstract
In this paper, we prove that if $K$ is a nonempty weakly compact set in a Banach space $X$, $T:K\to K$ is a nonexpansive map satisfying $\frac{x+Tx}{2}\in K$ for all $x\in K$ and if $X$ is $3-$uniformly convex or $X$ has the Opial property, then $T$ has a fixed point in $K.$Downloads
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